NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.1 - Multiple Choice Questions
Question 5

Question. 5

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A)

(B)

(C)

875

(D)

1750

If the number is \(d\), then:

When 70 is divided by \(d\), remainder = 5. This means \(d\) divides \(70 - 5 = 65\).

When 125 is divided by \(d\), remainder = 8. This means \(d\) divides \(125 - 8 = 117\).

So \(d\) must be a common divisor of 65 and 117.

The HCF of 65 and 117 is 13. Hence, the required number is 13.